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This balanced and comprehensive study presents the theory, methods and applications of matrix analysis in a new theoretical framework, allowing readers to understand second-order and higher-order matrix analysis in a completely new light. Alongside the core subjects in matrix analysis, such as singular value analysis, the solution of matrix equations and eigenanalysis, the author introduces new applications and perspectives that are unique to this book. The very topical subjects of gradient analysis and optimization play a central role here. Also included are subspace analysis, projection analysis and tensor analysis, subjects which are often neglected in other books. Having provided a solid foundation to the subject, the author goes on to place particular emphasis on the many applications matrix analysis has in science and engineering, making this book suitable for scientists, engineers and graduate students alike.

Matrices --- Matrix analytic methods

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Analytical chemistry --- Biochemistry --- Analysis, Chemical --- Analytic chemistry --- Chemical analysis --- Chemistry, Analytic --- Chemistry --- Technique. --- Technological innovations.

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Chemometrics. --- Chemistry --- Analytical chemistry. --- Analysis, Chemical --- Analytic chemistry --- Chemical analysis --- Chemistry, Analytic --- Analytical chemistry --- Mathematics. --- Mathematics --- Measurement --- Statistical methods

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Variational inequalities (Mathematics) --- Mechanics, Analytic. --- Analytical mechanics --- Kinetics --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities

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The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various "radii of analyticity"). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.

p-adic analysis. --- p-adic groups. --- Representations of groups. --- Geometry, Analytic.